Publication 26-CNA-017

How Does Hard Magnetic Soft Matter Deform?

Daniel Katusele
Program in Computational Mechanics and
Department of Civil and Environmental Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
dkatusel@andrew.cmu.edu

Carmel Majidi
Department of Mechanical Engineering
Carnegie Mellon University
Pittsburgh, PA 15213

Liping Liu
Department of Mathematics
Rutgers University
NJ 08854, USA

Pradeep Sharma
Department of Mechanical Engineering
University of Houston
Houston, Texas 77004
psharma@uh.edu

Kaushik Dayal
Department of Civil and Environmental Engineering
Center for Nonlinear Analysis
Department of Mechanical Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
Kaushik.Dayal@cmu.edu

Abstract: Hard Magnetic Soft Materials, i.e., elastomers seeded with hard magnetic particles, convert magnetic energy into complex motion and have become central to the design of untethered soft robots, biomedical devices, and, in general, for enabling fast, wireless actuation. Their behavior depends critically on how the surrounding soft matrix deforms and transmits torque to each magnetized inclusion, yet there is no consensus on the correct mapping between macroscopic strain and microscopic motion. Competing models predict conflicting particle rotations and magnetic responses under identical loads. Here, we construct counterexamples that show the key shortcomings in these models, and then establish a first-principles framework that leads to an optimal deformation mapping. The resulting closed-form law unifies conflicting models and shows that they are, in fact, simply different limits of our general approach. Our work permits the rational design of magnetically actuated soft devices and a unified view of deformation in magnetic soft matter, and broadly, in similar architectured materials.

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